Related papers: Basic statistics for probabilistic symbolic variab…
A common feature of methods for analyzing samples of probability density functions is that they respect the geometry inherent to the space of densities. Once a metric is specified for this space, the Fr\'echet mean is typically used to…
A novel variational inference based resampling framework is proposed to evaluate the robustness and generalization capability of deep learning models with respect to distribution shift. We use Auto Encoding Variational Bayes to find a…
Robust statistics traditionally focuses on outliers, or perturbations in total variation distance. However, a dataset could be corrupted in many other ways, such as systematic measurement errors and missing covariates. We generalize the…
Discrepancy measures between probability distributions, often termed statistical distances, are ubiquitous in probability theory, statistics and machine learning. To combat the curse of dimensionality when estimating these distances from…
We study quantum statistical inference tasks of hypothesis testing and their canonical variations, in order to review relations between their corresponding figures of merit---measures of statistical distance---and demonstrate the crucial…
We propose to align distributional data from the perspective of Wasserstein means. We raise the problem of regularizing Wasserstein means and propose several terms tailored to tackle different problems. Our formulation is based on the…
We provide new convergence guarantees in Wasserstein distance for diffusion-based generative models, covering both stochastic (DDPM-like) and deterministic (DDIM-like) sampling methods. We introduce a simple framework to analyze…
In this paper we consider a variety of procedures for numerical statistical inference in the family of univariate and multivariate stable distributions. In connection with univariate distributions (i) we provide approximations by finite…
Statistical inference can be performed by minimizing, over the parameter space, the Wasserstein distance between model distributions and the empirical distribution of the data. We study asymptotic properties of such minimum Wasserstein…
Nowadays stochastic computer simulations with both numeral and distribution inputs are widely used to mimic complex systems which contain a great deal of uncertainty. This paper studies the design and analysis issues of such computer…
Motivated by the statistical and computational challenges of computing Wasserstein distances in high-dimensional contexts, machine learning researchers have defined modified Wasserstein distances based on computing distances between…
This paper builds Wasserstein ambiguity sets for the unknown probability distribution of dynamic random variables leveraging noisy partial-state observations. The constructed ambiguity sets contain the true distribution of the data with…
The Wasserstein distance between two probability measures on a metric space is a measure of closeness with applications in statistics, probability, and machine learning. In this work, we consider the fundamental question of how quickly the…
We study the Wasserstein distance of order 1 between the empirical distribution and the marginal distribution of stationary $\alpha$-dependent sequences. We prove some moments inequalities of order p for any p $\ge$ 1, and we give some…
Computer experiments are becoming increasingly important in scientific investigations. In the presence of uncertainty, analysts employ probabilistic sensitivity methods to identify the key-drivers of change in the quantities of interest.…
We study the weighted total variation distance between probability measures. Using Fourier-analytic tools, we present estimates in terms of Wasserstein distances between the respective probabilities, under appropriate smoothness and moment…
We develop a general framework for statistical inference with the 1-Wasserstein distance. Recently, the Wasserstein distance has attracted considerable attention and has been widely applied to various machine learning tasks because of its…
Motivated by the growing popularity of variants of the Wasserstein distance in statistics and machine learning, we study statistical inference for the Sliced Wasserstein distance--an easily computable variant of the Wasserstein distance.…
The prior distribution is a crucial building block in Bayesian analysis, and its choice will impact the subsequent inference. It is therefore important to have a convenient way to quantify this impact, as such a measure of prior impact will…
We introduce the observable Wasserstein distance, a framework for deriving lower bounds on the Wasserstein distance between probability measures on Polish metric spaces, designed to bypass the computational intractability of exact optimal…